Involutive MCMC: a Unifying Framework

Abstract

Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. The field has developed a broad spectrum of algorithms, varying in the way they are motivated, the way they are applied and how efficiently they sample. Despite all the differences, many of them share the same core principle, which we unify as the Involutive MCMC (iMCMC) framework. Building upon this, we describe a wide range of MCMC algorithms in terms of iMCMC, and formulate a number of "tricks" which one can use as design principles for developing new MCMC algorithms. Thus, iMCMC provides a unified view of many known MCMC algorithms, which facilitates the derivation of powerful extensions. We demonstrate the latter with two examples where we transform known reversible MCMC algorithms into more efficient irreversible ones.

References in corpus (5)

• NICE: Non-linear Independent Components Estimation
• NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport
• A Comparison of Methods for Computing Autocorrelation Time
• Driving Markov chain Monte Carlo with a dependent random stream
• How to view an MCMC simulation as a permutation, with applications to parallel simulation and improved importance sampling